where GRU denotes the GRU cell [1]} with LayerNorm [2]}, \(V, B, C \in \mathbb {R}^{d \times d}\)  are other learnable parameters, Aggr represents the neighborhood aggregation function (we use Max), \(\sigma \)  is the sigmoid function, and \(\odot \)  is the Hadamard product.
As inputs \(h_i^{\ell =0}\)  and \(e_{ij}^{\ell =0}\) , we use \(d\) -dimensional linear projections of the node coordinate \(x_i\)  and the euclidean distance \(\Vert x_i - x_j\Vert _2\) , respectively.
We generate predictions using the AR decoder after an arbitrary number of message passing steps \(L\) .
